Data that can be represented as a network, where there are measurements both on units and on pairs of units, are becoming increasingly prevalent in the social sciences and public health. Homophily in network data, or the tendency of units to connect based on similar nodal attribute values (i.e. income, HIV status) more often than expected by chance is receiving strong attention from researchers in statistics, medicine, sociology, public health and others. Respondent-Driven Sampling (RDS) is a link-tracing network sampling strategy heavily used in public health worldwide that is cost efficient and allows us to survey populations inaccessible by conventional techniques. Via extensive simulation we study the performance of existing methods of estimating population averages, and show that they have poor performance if there is homophily on the quantity surveyed. We propose the first model-based approach for this setting and show its superiority as a point estimator and in terms of uncertainty intervals coverage rates, and demonstrate its application to a real life RDS-based survey. We study how the strength of homophily effects can be estimated and compared across networks and different binary attributes under several network sampling schemes. We give a proof that homophily can be effectively estimated under RDS and propose a new homophily index. This work moves towards a deeper understanding of network structure as a function of nodal attributes and network sampling under homophily. / Statistics

Graduation date: 2006 / This research addresses sample process variance estimation on continuous domains and for non-probability samples in particular. The motivation for the research is a scenario in which a program has collected non-probability samples for which there is interest in characterizing how much an extrapolation to the domain would vary given similarly arranged collections of observations. This research does not address the risk of bias and a key assumption is that the observations could represent the response on the domain of interest. This excludes any hot-spot monitoring programs. The research is presented as a collection of three manuscripts. The first (to be published in Environmetrics (2006)) reviews and compares model- and design-based approaches for sampling and estimation in the context of continuous domains and promotes a model-assisted sample-process variance estimator. The next two manuscripts are written to be companion papers. With the objective of quantifying uncertainty of an estimator based on a non-probability sample, the proposed approach is to first characterize a class of sets of locations that are similarly arranged to the collection of locations in the non-probability sample, and then to predict variability of an estimate over that class of sets using the covariance structure indicated by the non-probability sample (assuming the covariance structure is indicative of the covariance structure on the study region). The first of the companion papers discusses characterizing classes of similarly arranged sets with the specification of a metric density. Goodness-of-fit tests are demonstrated on several types of patterns (dispersed, random and clustered) and on a non-probability collection of locations surveyed by Oregon Department of Fish & Wildlife on the Alsea River basin in Oregon. The second paper addresses predicting the variability of an estimate over sets in a class of sets (using a Monte Carlo process on a simulated response with appropriate covariance structure).